LAKE LURE, N.C.—North Carolina is close to dropping one of the most extensive programs for awarding tax breaks to film companies, in what would be a high-profile retreat from an arms race among states to lure Hollywood productions.

More than 800 movies and television shows have been filmed in North Carolina since the 1980s, when "Dirty Dancing" was shot along the banks of this mountain-ringed lake. The state started offering incentives in the early 2000s. In 2012, it paid $69 million in incentives to draw such...